SM_PDF_chapter30 - Nuclear Physics CHAPTER OUTLINE 30.1...

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823 Nuclear Physics CHAPTER OUTLINE 30.1 Some Properties of Nuclei 30.2 Binding Energy 30.3 Radioactivity 30.4 The Radioactive Decay Processes 30.5 Nuclear Reactions 30.6 Context Connection The Engine of the Stars ANSWERS TO QUESTIONS Q30.1 Because of electrostatic repulsion between the positively-charged nucleus and the +2 e alpha particle. To drive the α -particle into the nucleus would require extremely high kinetic energy. Q30.2 Nuclei with more nucleons than bismuth-209 are unstable because the electrical repulsion forces among all of the protons is stronger than the nuclear attractive force between nucleons. Q30.3 Extra neutrons are required to overcome the increasing electrostatic repulsion of the protons. The neutrons participate in the net attractive effect of the nuclear force, but feel no Coulomb repulsion. Q30.4 The nuclear force favors the formation of neutron-proton pairs, so a stable nucleus cannot be too far away from having equal numbers of protons and neutrons. This effect sets the upper boundary of the zone of stability on the neutron-proton diagram. All of the protons repel one another electrically, so a stable nucleus cannot have too many protons. This effect sets the lower boundary of the zone of stability. Q30.5 4 He , 16 O , 40 Ca , and 208 Pb. Q30.6 If one half the number of radioactive nuclei decay in one year, then one half the remaining number will decay in the second year. Three quarters of the original nuclei will be gone, and one quarter will remain. Q30.7 Since the samples are of the same radioactive isotope, their half-lives are the same. When prepared, sample A has twice the activity (number of radioactive decays per second) of sample B. After 5 half- lives, the activity of sample A is decreased by a factor of 2 5 , and after 5 half-lives the activity of sample B is decreased by a factor of 2 5 . So after 5 half-lives, the ratio of activities is still 2:1. Q30.8 The statement is false. Both patterns show monotonic decrease over time, but with very different shapes. For radioactive decay, maximum activity occurs at time zero. Cohorts of people now living will be dying most rapidly perhaps forty years from now. Everyone now living will be dead within less than two centuries, while the mathematical model of radioactive decay tails off exponentially forever. A radioactive nucleus never gets old. It has constant probability of decay however long it has existed.
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824 Nuclear Physics Q30.9 The alpha particle and the daughter nucleus carry equal amounts of momentum in opposite directions. Since kinetic energy can be written as p m 2 2 , the small-mass alpha particle has much more of the decay energy than the recoiling nucleus. Q30.10 Yes. The daughter nucleus can be left in its ground state or sometimes in one of a set of excited states. If the energy carried by the alpha particle is mysteriously low, the daughter nucleus can quickly emit the missing energy in a gamma ray.
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SM_PDF_chapter30 - Nuclear Physics CHAPTER OUTLINE 30.1...

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